The response of a laminar, premixed flame to perturbations of upstream equivalence ratio is investigated and modelled, with emphasis on the generation of ‘entropy waves’, i.e. entropic inhomogeneities of downstream temperature. Transient computational fluid dynamics simulations of two adiabatic lean methane-air flames of different Péclet numbers provide guidance and validation data for subsequent modelling. The respective entropy transfer functions, which describe the production of temperature inhomogeneities, as well as transfer functions for the variation of the heat release, are determined from the computational fluid dynamics time series data by means of system identification. The processes governing the dynamics of the entropy transfer functions are segregated into two sub-problems: (1) heat release due to chemical reaction at the flame front and (2) advective and diffusive transport. By adopting a formulation in terms of a mixture fraction variable, these two sub-problems can be treated independently from each other. Models for both phenomena are derived and analysed using simple 0- and 1-dimensional configurations. The heat release process (1) is represented by a fast-reaction-zone model, which takes into account variations of the specific heat capacity with equivalence ratio in order to evaluate the magnitude of downstream temperature fluctuations with quantitative accuracy. For the transport processes (2), two types of models based on mean field data from the computational fluid dynamics simulation are proposed: A semi-analytical, low-order formulation based on stream lines, and a state-space formulation, which is constructed by Finite Elements discretisation of the transport equation for mixture fraction. Model predictions for the entropy transfer functions are found to agree well with the computational fluid dynamics reference data at very low computational costs.

中文翻译：

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通过预混火焰模拟温度不均匀性的产生

对层流，预混火焰对上游当量比扰动的响应进行了研究和建模，重点是“熵波”的产生，即下游温度的熵不均匀。两个不同佩克利特数的绝热贫甲烷-空气火焰的瞬态计算流体动力学模拟为后续建模提供了指导和验证数据。通过系统识别从计算流体动力学时间序列数据中确定相应的熵传递函数，这些熵传递函数描述了温度不均匀性的产生以及热量释放变化的传递函数。控制熵传递函数动力学的过程分为两个子问题：（1）由于火焰前沿的化学反应而释放的热量，以及（2）对流和扩散传输。通过采用关于混合分数变量的公式，这两个子问题可以彼此独立地处理。使用简单的0维和1维配置可以导出和分析这两种现象的模型。放热过程（1）以快速反应区模型表示，该模型考虑了比热容随当量比的变化，以便以定量精度评估下游温度波动的幅度。对于运输过程（2），提出了两种基于计算流体动力学模拟的平均场数据的模型：基于流线的半解析低阶公式和状态空间公式，它是通过混合分数的输运方程的离散化有限元构造的。发现熵传递函数的模型预测与计算流体动力学参考数据非常吻合，而计算成本却非常低。